Benoit Mandelbrot

{{External media |float=right | width=210px |headerimage=210px | video1=[http://www.webofstories.com/play/benoit.mandelbrot/1;jsessionid=E8EB8E149375B3987E49D5E4F02FCB57 Family background and early education], (4:11) Benoit Mandelbrot interview, Part 1 of 144, Web of Stories{{cite web |url=http://www.webofstories.com/play/9596 |title=Web of Stories – Benoît Mandelbrot – Family background and early education |last=Mandelbrot |first=Benoît |author2=Bernard Sapoval |author3=Daniel Zajdenweber |date=May 1998 |publisher=Web of Stories |access-date=19 October 2010 |archive-date=11 September 2011 |archive-url=https://web.archive.org/web/20110911162528/http://www.webofstories.com/play/9596 |url-status=live }}}}

Benedykt Mandelbrot{{Cite journal | last = Gołąb-Meyer | first = Zofia | title = Benoit Mandelbrot (1924–2010) – ojciec geometrii fraktalnej | url = http://www.foton.if.uj.edu.pl/documents/12579485/8a780912-d415-4ece-8f8c-59b8134ca4a1 | journal = Foton | publisher = Instytut Fizyki Uniwersytetu Jagiellońskiego | volume = 112 | date =Spring 2011 | page = 50 | access-date= 25 December 2021}} was born in a Lithuanian Jewish family, in Warsaw during the Second Polish Republic.{{Cite news|last=Hoffman|first=Jascha|date=16 October 2010|title=Benoît Mandelbrot, Novel Mathematician, Dies at 85 (Published 2010)|language=en-US|work=The New York Times|url=https://www.nytimes.com/2010/10/17/us/17mandelbrot.html|access-date=20 November 2020|issn=0362-4331|archive-date=21 January 2017|archive-url=https://web.archive.org/web/20170121082521/http://www.nytimes.com/2010/10/17/us/17mandelbrot.html|url-status=live}} His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me."{{cite web |last=Mandelbrot |first=Benoît |title=The Wolf Prizes for Physics, A Maverick's Apprenticeship |publisher=Imperial College Press |year=2002 |url= http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf |access-date=23 April 2012 |archive-date=3 December 2013 |archive-url= https://web.archive.org/web/20131203024639/http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf |url-status=live }}

In 1936, when he was 11, the family emigrated from Poland to France. The move, World War II, and the influence of his father's brother, the mathematician Szolem Mandelbrojt (who had moved to Paris around 1920), further prevented a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes.{{rp|17}}{{cite news|url=https://www.bbc.co.uk/news/world-europe-11560101| title= 'Fractal' mathematician Benoît Mandelbrot dies aged 85|date=17 October 2010|work=BBC Online|access-date=17 October 2010|archive-date=18 October 2010|archive-url= https://web.archive.org/web/20101018045143/http://www.bbc.co.uk/news/world-europe-11560101|url-status=live}}

Mandelbrot attended the Lycée Rollin (now the Collège-lycée Jacques-Decour) in Paris until the start of World War II, when his family moved to Tulle, France. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies.{{rp|62–63}}{{cite book| last= Hemenway| first= P. |year= 2005| title= Divine proportion: Phi in art, nature and science| publisher= Psychology Press |isbn= 0-415-34495-6}} Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period:

{{blockquote|Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why?{{rp|49}}}}

In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc in Lyon, and in 1945 to 1947 attended the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master's degree in aeronautics. Returning to France, he obtained his PhD degree in Mathematical Sciences at the University of Paris in 1952.

From 1949 to 1958, Mandelbrot was a staff member at the Centre National de la Recherche Scientifique. During this time he spent a year at the Institute for Advanced Study in Princeton, New Jersey, where he was sponsored by John von Neumann. In 1955 he married Aliette Kagan and moved to Geneva, Switzerland (to collaborate with Jean Piaget at the International Centre for Genetic Epistemology) and later to the Université Lille Nord de France.{{Cite web|first= B. B. |last= Mandelbrot| interviewer= Anthony Barcellos |title=Mathematical People, Interview of B. B. Mandelbrot |publisher= Birkhaüser| year=1984|url=http://users.math.yale.edu/~bbm3/web_pdfs/inHisOwnWords.pdf|access-date=25 June 2013|archive-date=27 April 2015|archive-url= https://web.archive.org/web/20150427164851/http://users.math.yale.edu/~bbm3/web_pdfs/inHisOwnWords.pdf|url-status=live}} In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York. He remained at IBM for 35 years, becoming an IBM Fellow, and later Fellow Emeritus.

From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory, economics, and fluid dynamics.

Mandelbrot saw financial markets as an example of "wild randomness", characterized by concentration and long-range dependence. He developed several original approaches for modelling financial fluctuations.{{cite encyclopedia |last1=Cont |first1=Rama |title=Mandelbrot, Benoit |encyclopedia=Encyclopedia of Quantitative Finance |date=15 May 2010 |pages=eqf01006 |doi=10.1002/9780470061602.eqf01006|isbn = 9780470057568}} In his early work, he found that the price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.{{cite web |url=https://www.newscientist.com/article/mg15420784.700-flight-over-wall-st.html |title= New Scientist'', 19 April 1997 |publisher=Newscientist.com |date=19 April 1997 |access-date=17 October 2010 |archive-date=21 April 2010 |archive-url= https://web.archive.org/web/20100421101729/http://www.newscientist.com/article/mg15420784.700-flight-over-wall-st.html |url-status=live }} The latter work from the early 60s was done with daily data of cotton prices from 1900, long before he introduced the word 'fractal'. In later years, after the concept of fractals had matured, the study of financial markets in the context of fractals became possible only after the availability of high frequency data in finance.

In the late 1980s, Mandelbrot used intra-daily tick data supplied by Olsen & Associates in Zurich{{Cite journal |last= Davidson |first= Clive |date= 15 December 1997 |title= Wildly Random Market Moves |url= https://www.joc.com/wildly-random-market-moves_19971215.html |journal= Journal of Commerce |via= JOC.com |access-date= |archive-date= 11 July 2021 |archive-url= https://web.archive.org/web/20210711170709/https://www.joc.com/wildly-random-market-moves_19971215.html |url-status= dead }}{{Cite web| last= Muldoon| first= Oliver |date= 14 October 2019|title=The Wandering Scientist Turned Father of Fractals| url=https://medium.com/swlh/the-wandering-scientist-turned-father-of-fractals-4dcdc867d4dd|access-date=19 March 2021| website= Medium.com |language=en}} to apply fractal theory to market microstructure. This cooperation led to the publication of the first comprehensive papers on scaling law in finance.{{Cite journal| last1= Müller| first1= Ulrich A.|last2=Dacorogna|first2=Michel M.|last3=Olsen|first3=Richard B.|last4=Pictet|first4=Oliver V.|last5=Schwarz|first5=Matthias|last6=Morgenegg|first6=Claude|date=Dec 1990|title=Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis|url=https://doi.org/10.1016/0378-4266(90)90009-Q|journal=Journal of Banking and Finance|volume=14|issue=6|pages=1189–1208| doi=10.1016/0378-4266(90)90009-Q|via=Elsevier Science Direct}}{{Cite journal|last1=Müller|first1=U. A.|last2=Dacorogna|first2=M. M.|last3=Davé|first3=R. D.|last4=Pictet|first4=O. V.| last5= Olsen| first5= R. B.|last6=Ward|first6=J. R.|date=28 June 1995|title=FRACTALS AND INTRINSIC TIME – A CHALLENGE TO ECONOMETRICIANS| journal= Opening Lecture of the XXXIXth International Conference of the Applied Econometrics Association |citeseerx=10.1.1.197.2969}} This law shows similar properties at different time scales, confirming Mandelbrot's insight of the fractal nature of market microstructure. Mandelbrot's own research in this area is presented in his books Fractals and Scaling in Finance{{Cite book| last= Mandelbrot| first= Benoit|title=Fractals and Scaling in Finance|publisher=Springer|year=1997|isbn=978-1-4757-2763-0}} and The (Mis)behavior of Markets.{{Cite book| last= Mandelbrot |first= Benoit| title= The (Mis)behavior of Markets|publisher=Profile Books|year=2004|isbn=9781861977656}}

As a visiting professor at Harvard University, Mandelbrot began to study mathematical objects called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the Mandelbrot set which was introduced by him in 1979.

File:Mandelbrot p1130876.jpg, during his acceptance speech for the Légion d'honneur in 2006]]

In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas in the French book Les Objets Fractals: Forme, Hasard et Dimension, later translated in 1977 as Fractals: Form, Chance and Dimension.Fractals: Form, Chance and Dimension, by Benoît Mandelbrot; W H Freeman and Co, 1977; {{isbn|0-7167-0473-0}} According to computer scientist and physicist Stephen Wolfram, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before".{{cite news| last= Wolfram| first= Stephen| url= https://www.wsj.com/articles/SB10001424127887324439804578107271772910506 |title= The Father of Fractals| archiveurl= https://web.archive.org/web/20170825102714/https://www.wsj.com/articles/SB10001424127887324439804578107271772910506 |archivedate=25 August 2017 | work= The Wall Street Journal| date= 22 November 2012| access-date= }} Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals":

{{blockquote|Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.}}

Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesque broccoli are two examples from nature." He points out an unexpected conclusion:

{{blockquote|One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot.}}

Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphics computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s psychedelic art with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist Johannes Kepler, who calculated and described the orbits of the planets.{{cite web| last= Ivry| first= Benjamin| url= http://forward.com/articles/166094/benoit-mandelbrot-influenced-art-and-mathematics/?p=all |title= Benoit Mandelbrot Influenced Art and Mathematics| archiveurl= https://web.archive.org/web/20130602171300/http://forward.com/articles/166094/benoit-mandelbrot-influenced-art-and-mathematics/?p=all |archivedate= 2 June 2013 | website=The Jewish Daily Forward | date= 17 November 2012| access-date= }}

File:Newton-lplane-Mandelbrot.jpg

Mandelbrot, however, never felt he was inventing a new idea. He described his feelings in a documentary with science writer Arthur C. Clarke:

{{blockquote|Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.{{citation| url= https://www.youtube.com/watch?v=Lk6QU94xAb8 |title= Arthur C Clarke – Fractals – The Colors Of Infinity|date= 25 December 2010| archiveurl= https://web.archive.org/web/20170531193057/https://www.youtube.com/watch?v=Lk6QU94xAb8 |archivedate= 31 May 2017 | access-date= | via= YouTube}}}}

According to Clarke, "the Mandelbrot set is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity?" Clarke also notes an "odd coincidence":

the name Mandelbrot, and the word "mandala"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas.

In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature.{{cite book| url= https://books.google.com/books?id=xJ4qiEBNP4gC |title= The Fractal Geometry of Nature |archiveurl= https://web.archive.org/web/20151130231048/https://books.google.com/books?id=xJ4qiEBNP4gC&printsec=frontcover |archivedate=30 November 2015 | first= Benoît| last= Mandelbrot| publisher= W H Freeman & Co| year= 1982 |isbn= 0-7167-1186-9}} This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".

Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division.{{cite web|url=http://www.webofstories.com/play/10483|title=Benoît Mandelbrot • IBM: background and policies |last=Mandelbrot |first=Benoît |author2=Bernard Sapoval |author3=Daniel Zajdenweber|date=May 1998|publisher=Web of Stories|access-date=17 October 2010|archive-date=8 September 2011|archive-url=https://web.archive.org/web/20110908162215/http://www.webofstories.com/play/10483|url-status=live}} He joined the Department of Mathematics at Yale, and obtained his first tenured post in 1999, at the age of 75.{{cite news|url=https://www.theatlantic.com/technology/archive/2010/10/benoit-mandelbrot-the-maverick-1924-2010/64684/|title=Benoît Mandelbrot the Maverick, 1924–2010|last=Tenner|first=Edward|date=16 October 2010|work=The Atlantic|access-date=16 October 2010|archive-date=18 October 2010|archive-url= https://web.archive.org/web/20101018132145/http://www.theatlantic.com/technology/archive/2010/10/benoit-mandelbrot-the-maverick-1924-2010/64684/|url-status=live}} At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.

Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.{{rp|xi}} He began by asking himself various kinds of questions related to nature:

{{blockquote|Can geometry deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?{{cite book| last= Mandelbrot| first= Benoit |year= 2012| title= The Fractalist: Memoir of a Scientific Maverick| publisher= Pantheon Books |isbn= 978-0-307-38991-6}}{{rp|xii}}}}

In his paper "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", published in Science in 1967, Mandelbrot discusses self-similar curves that have Hausdorff dimension that are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.{{cite news| quote= Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?"| url= https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-/vD0Sjafcl9t9BNghRf8Qw |title= Benoît Mandelbrot, Novel Mathematician, Dies at 85| archiveurl= https://web.archive.org/web/20181231150228/https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-%2FvD0Sjafcl9t9BNghRf8Qw |archivedate=31 December 2018 | work= The New York Times| date= 17 October 2010| access-date= }}{{cite journal | title=How long is the coast of Britain? Statistical self-similarity and fractional dimension | journal=Science | date=5 May 1967 | last= Mandelbrot| first= Benoit B. | pages=636–638 | volume=156 | issue=3775 | doi=10.1126/science.156.3775.636 | pmid=17837158 | url= http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf | bibcode=1967Sci...156..636M | s2cid=15662830 | access-date=11 January 2016 | archive-date=13 July 2015 | archive-url=https://web.archive.org/web/20150713023120/http://www.sciencemag.org/content/156/3775/636 | url-status=live }}

Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that "real roughness is often fractal and can be measured."{{rp|296}} Although Mandelbrot coined the term "fractal", some of the mathematical objects he presented in The Fractal Geometry of Nature had been previously described by other mathematicians. Before Mandelbrot, however, they were regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to explaining non-smooth, "rough" objects in the real world. His methods of research were both old and new:

{{blockquote|The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer ... bringing an element of unity to the worlds of knowing and feeling ... and, unwittingly, as a bonus, for the purpose of creating beauty.{{rp|292}}}}

Fractals are also found in human pursuits, such as music, painting, architecture, and in the financial field. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry:

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
  —Mandelbrot, in his introduction to The Fractal Geometry of Nature

File:Mandel zoom 08 satellite antenna.jpg

Mandelbrot has been called an artist, and a visionary{{cite journal| last= Devaney| first= Robert L.|author-link= Robert L. Devaney |title= Mandelbrot's Vision for Mathematics| journal= Proceedings of Symposia in Pure Mathematics| volume= 72| number= 1 |publisher=American Mathematical Society |year=2004 |url=http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf |access-date=5 January 2007 |url-status=dead |archive-url= https://web.archive.org/web/20061209093734/http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf |archive-date=9 December 2006 }} and a maverick.{{cite web| url= https://www.pbs.org/wgbh/nova/fractals/mandelbrot.html| title=A Radical Mind| last=Jersey| first=Bill |date=24 April 2005|work=Hunting the Hidden Dimension, NOVA|publisher= PBS|access-date=20 August 2009 |archive-date= 22 August 2009|archive-url=https://web.archive.org/web/20090822022402/http://www.pbs.org/wgbh/nova/fractals/mandelbrot.html|url-status=live}} His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.

Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.{{cite journal| title= Galaxy Map Hints at Fractal Universe| first= Amanda |last= Gefter| journal= New Scientist| date= 25 June 2008| url= | access-date= }}

Mandelbrot's awards include the Wolf Prize in Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003,[http://www.japanprize.jp/en/laureates_by_year2000.html Laureates of the Japan Prize] {{Webarchive|url=https://web.archive.org/web/20160417143540/http://www.japanprize.jp/en/laureates_by_year2000.html |date=17 April 2016 }}. japanprize.jp and the Einstein Lectureship of the American Mathematical Society in 2006.

The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Chevalier in France's Legion of Honour. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory.{{cite press release |url=http://www.pnl.gov/news/release.asp?id=141 |title= Mandelbrot joins Pacific Northwest National Laboratory |publisher= Pacific Northwest National Laboratory | website= pnl.gov |date=16 February 2006 |access-date=17 October 2010 |archive-date=12 January 2009 |archive-url= https://web.archive.org/web/20090112155340/http://www.pnl.gov/news/release.asp?id=141 |url-status= live }} Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006.{{cite web |url= http://www.legifrance.gouv.fr/WAspad/UnTexteDeJorf?numjo=PREX0508911D |title=Légion d'honneur announcement of promotion of Mandelbrot to officier |language=fr |publisher=Legifrance.gouv.fr |access-date=17 October 2010 |archive-date=20 November 2020 |archive-url=https://web.archive.org/web/20201120141436/https://www.legifrance.gouv.fr/jorf/id/JORFTEXT000000456787 |url-status=live }} An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises.{{cite web |url=http://gazette.jhu.edu/2010/06/07/six-granted-honorary-degrees-society-of-scholars-inductees-recognized-2/ |title=Six granted honorary degrees, Society of Scholars inductees recognized |publisher= Johns Hopkins University| website= gazette.jhu.edu |date=7 June 2010 |access-date=17 October 2010 |archive-date=17 June 2010 |archive-url= https://web.archive.org/web/20100617164139/http://gazette.jhu.edu/2010/06/07/six-granted-honorary-degrees-society-of-scholars-inductees-recognized-2/ |url-status=live }}

A partial list of awards received by Mandelbrot:{{cite web | last= Mandelbrot| first= Benoit B. | title=Vita and Awards | format= Word document | date=2 February 2006| url= http://math.yale.edu/mandelbrot/web_docs/VitaSeveralPage.doc | archiveurl= https://web.archive.org/web/20070702211144/http://math.yale.edu/mandelbrot/web_docs/VitaSeveralPage.doc | archivedate= 2 July 2007 | access-date= 15 December 2013}}

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• 2004 Best Business Book of the Year Award
• AMS Einstein Lectureship
• Barnard Medal
• Caltech Service
• Casimir Funk Natural Sciences Award
• Charles Proteus Steinmetz Medal
• High School Spelling Bee (1940)
• Fellow, American Geophysical Union
• Fellow of the American Statistical Association{{cite web| url= http://www.amstat.org/awards/fellowslist.cfm | title= View/Search Fellows of the ASA| website= amstat.org| archiveurl= https://web.archive.org/web/20160616161612/https://www.amstat.org/awards/fellowslist.cfm |archivedate=16 June 2016 |accessdate= 20 August 2016}}
• Fellow of the American Physical Society (1987) {{cite web|url=https://www.aps.org/programs/honors/fellowships/archive-all.cfm?initial=&year=1987&unit_id=&institution=|title=APS Fellow Archive| publisher= APS| access-date=24 September 2020|archive-date=20 November 2020|archive-url=https://web.archive.org/web/20201120141515/https://www.aps.org/programs/honors/fellowships/archive-all.cfm?initial=&year=1987&unit_id=&institution=|url-status=live}}
• Franklin Medal
• Harvey Prize (1989)
• Honda Prize
• Humboldtpreis
• IBM Fellowship
• Japan Prize (2003)
• John Scott Award
• Légion d'honneur (Legion of Honour)
• Lewis Fry Richardson Medal
• Medaglia della Presidenza della Repubblica Italiana
• Médaille de Vermeil de la Ville de Paris
• Nevada Prize
• Member of the Norwegian Academy of Science and Letters.{{cite web|url=http://www.dnva.no/c26849/artikkel/vis.html?tid=40116|title=Gruppe 1: Matematiske fag|publisher=Norwegian Academy of Science and Letters|language=no|access-date=7 October 2010|archive-date=10 November 2013|archive-url=https://web.archive.org/web/20131110152102/http://www.dnva.no/c26849/artikkel/vis.html?tid=40116|url-status=live}}
• Member of the American Philosophical Society (2004) {{cite web|url=https://search.amphilsoc.org/memhist/search?creator=Benoit+B.+Mandelbrot&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|title=American Philosophical Society Member History |access-date=14 June 2021}}
• Science for Art
• Sven Berggren-Priset
• Wacław Sierpiński medal of the Polish Mathematical Society (2005) {{cite web|url=https://www.ptm.org.pl/konkursy/wyklady-im-waclawa-sierpinskiego|access-date=21 January 2023|title=Medal i Wykład im. Wacława Sierpińskiego | Polskie Towarzystwo Matematyczne }}
• Władysław Orlicz Prize
• Wolf Prize in Physics (1993)

{{div col end}}

Mandelbrot died from pancreatic cancer at the age of 85 in a hospice in Cambridge, Massachusetts, on 14 October 2010.{{cite news |title=Benoît Mandelbrot, fractals pioneer, dies |url=http://www.upi.com/Science_News/2010/10/16/Benoit-Mandelbrot-fractals-pioneer-dies/UPI-11551287266964/ |access-date=17 October 2010 |newspaper=United Press International |date=16 October 2010 |archive-date=22 October 2012 |archive-url=https://web.archive.org/web/20121022020458/http://www.upi.com/Science_News/2010/10/16/Benoit-Mandelbrot-fractals-pioneer-dies/UPI-11551287266964/ |url-status=live }} Reacting to news of his death, mathematician Heinz-Otto Peitgen said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years."

Chris Anderson, TED conference curator, described Mandelbrot as "an icon who changed how we see the world".{{cite news |url=https://montrealgazette.com/technology/Mandelbrot+father+fractal+geometry+dies/3682961/story.html |title=Mandelbrot, father of fractal geometry, dies |work=The Gazette |access-date=16 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20101019233754/http://www.montrealgazette.com/technology/Mandelbrot%2Bfather%2Bfractal%2Bgeometry%2Bdies/3682961/story.html |archive-date=19 October 2010 }} Nicolas Sarkozy, President of France at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions [... h]is work, developed entirely outside mainstream research, led to modern information theory."{{cite news |url=http://www.lefigaro.fr/flash-actu/2010/10/16/97001-20101016FILWWW00611-sarkozy-rend-hommage-a-mandelbrot.php |title=Sarkozy rend hommage à Mandelbrot |language=fr |trans-title=Sarkozy pays homage to Mandelbrot |work=Le Figaro |access-date=17 October 2010 |archive-date=28 July 2013 |archive-url=https://web.archive.org/web/20130728181450/http://www.lefigaro.fr/flash-actu/2010/10/16/97001-20101016FILWWW00611-sarkozy-rend-hommage-a-mandelbrot.php |url-status=live }} Mandelbrot's obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".[http://www.economist.com/node/17305197 Benoît Mandelbrot's obituary] {{Webarchive|url=https://web.archive.org/web/20101024200744/http://www.economist.com/node/17305197 |date=24 October 2010 }}. The Economist (21 October 2010)

Best-selling essayist-author Nassim Nicholas Taleb has remarked that Mandelbrot's book The (Mis)Behavior of Markets is in his opinion "The deepest and most realistic finance book ever published".

• Fractals: Form, Chance and Dimension, 1977, 2020
• {{cite book |last1=Mandelbrot |first1=Benoît B. |title=The Fractal Geometry of Nature | year=1982 |publisher=W.H. Freeman |location=San Francisco |isbn=978-0-7167-1186-5|title-link=The Fractal Geometry of Nature }}
• Mandelbrot, B. (1959) Variables et processus stochastiques de Pareto-Levy, et la repartition des revenus. Comptes rendus de l'Académie des Sciences de Paris, 249, 613–615.
• Mandelbrot, B. (1960) The Pareto-Levy law and the distribution of income. International Economic Review, 1, 79–106.
• Mandelbrot, B. (1961) Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29, 517–543.
• Mandelbrot, B. (1964) Random walks, fire damage amount and other Paretian risk phenomena. Operations Research, 12, 582–585.
• Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E, 1997 by Benoit B. Mandelbrot and R.E. Gomory
• Mandelbrot, Benoit B. (1997) Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, Springer.
• Fractales, hasard et finance, 1959–1997, 1 November 1998
• Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976) (Selecta; V.N) 18 January 1999 by J.M. Berger and Benoit B. Mandelbrot
• {{cite journal |last=Mandelbrot |first=Benoît |date=February 1999 |title=A Multifractal Walk down Wall Street |journal=Scientific American | bibcode=1999SciAm.280b..70M |volume=280 |page=70 |doi=10.1038/scientificamerican0299-70 |issue=2}}
• Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot) 14 December 2001 by Benoit Mandelbrot and F.J. Damerau
• Mandelbrot, Benoit B., Gaussian Self-Affinity and Fractals, Springer: 2002.
• Fractals and Chaos: The Mandelbrot Set and Beyond, 9 January 2004
• Mandelbrot, Benoit B. (2010). [https://www.amazon.com/Fractalist-Memoir-Scientific-Maverick/dp/030738991X The Fractalist, Memoir of a Scientific Maverick.] New York: [http://www.randomhouse.com/highschool/catalog/display.pperl?isbn=9780307389916&view=email_prep Vintage Books], Division of Random House. {{isbn|978-0-307-38991-6}}
• The Fractalist: Memoir of a Scientific Maverick, 2014
• {{cite book |ref=Hudson|last1=Hudson |first1=Richard L. |last2=Mandelbrot |first2=Benoît B. |title=The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward |url= https://archive.org/details/misbehaviorofmar00beno|url-access=registration|year=2004 |publisher=Basic Books |location=New York |isbn=978-0-465-04355-2}}; (2006 {{ISBN|978-0465043576}})
• Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe and Cornelia Zahlten: Fractals: An Animated Discussion (63 min video film, interviews with Benoît Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990. {{isbn|0-7167-2213-5}} (re-published by Films for the Humanities & Sciences, {{isbn|978-0-7365-0520-8}})
• {{cite news |url=http://www.ft.com/cms/s/2/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html |title=A focus on the exceptions that prove the rule |last1=Mandelbrot |first1=Benoît |first2=Nassim |last2=Taleb |date=23 March 2006 |work=Financial Times |access-date=17 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20101023201028/http://www.ft.com/cms/s/2/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html |archive-date=23 October 2010 }}
• [https://www.pbs.org/wgbh/nova/fractals/ "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature"], NOVA, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.

{{columns-list|colwidth=35em|

• {{Annotated link|Pink noise|1/f noise}}
• {{Annotated link|Fractal dimension}}
• {{Annotated link|Fractional Brownian motion}}
• {{Annotated link|How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|How Long is the Coast of Britain?}}
• {{Annotated link|Hurst exponent}}
• {{Annotated link|Kurtosis risk}}
• {{Annotated link|Lacunarity}}
• List of Poles
• {{Annotated link|Louis Bachelier}}
• {{Annotated link|Mandelbrot Competition}}
• {{Annotated link|Multifractal system}}
• {{Annotated link|Self-similarity}}
• {{Annotated link|Seven states of randomness}}
• {{Annotated link|Skewness risk}}
• {{Annotated link|Zipf–Mandelbrot law}}

}}

{{notelist}}

{{Reflist}}

• {{cite book |last1=Frame |first1=Michael |last2=Cohen |first2=Nathan |title=Benoit Mandelbrot: A Life in Many Dimensions |year=2015 |publisher=World Scientific Publishing Company |location=Singapore |isbn=978-981-4366-06-9 }}

{{Commons|Benoît Mandelbrot}}

{{Wikiquote}}

• {{MathGenealogy|id=60791}}
• [http://users.math.yale.edu/mandelbrot/ Mandelbrot's page at Yale]
• [http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness.html "Benoît Mandelbrot: Fractals and the art of roughness"] {{Webarchive|url=https://web.archive.org/web/20140217132541/http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness.html |date=17 February 2014 }} (TED address).
• [http://video.mit.edu/watch/fractals-in-science-engineering-and-finance-roughness-and-beauty-9893/ Fractals in Science, Engineering and Finance] (lecture).
• [http://video.ft.com/v/63078298001/Why-efficient-markets-collapse-Mandelbrot FT.com interview] on the subject of the financial markets which includes his critique of the "efficient market" hypothesis.
• {{cite journal |journal=Physics Today |year=2011 |title=Obituaries: Benoit Mandelbrot |first1=Richard |last1=Taylor |volume=64 |issue=6 |doi=10.1063/1.3603925 |page=63 |bibcode=2011PhT....64f..63T |doi-access=free }}
• [http://www.webofstories.com/people/benoit.mandelbrot/1 Mandelbrot relates his life story] (Web of Stories).
• [http://dynkincollection.library.cornell.edu/biographies/882 Interview (1 January 1981, Ithaca, NY)] held by the Eugene Dynkin Collection of Mathematics Interviews, Cornell University Library.
• [https://www.youtube.com/watch?v=1o5FMTHkLQg Video animation of Mandelbrot set], zoom factor 10³⁴².
• {{YouTube|82xDvdgrzx0|Video animation of Mandelbulb}}, a three-dimensional Mandelbrot-set projection.
• {{YouTube|VB-XUoDqYfs|Video fly-through an animated Mandelbulb world}}
• {{IMDb name|541707}}
• {{TED speaker}}
• [http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/mandelbrot-benoit.pdf Michael Frame, "Benoit B. Mandelbrot", Biographical Memoirs of the National Academy of Sciences (2014)]

{{Wolf Prize in Physics}}

{{Japan Prize}}

{{Chaos theory}}

{{Fractals}}

{{Authority control}}

{{DEFAULTSORT:Mandelbrot, Benoit}}

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